Even worse, they're straw men. "Survival of the fittest" is merely an observation on how things tend to work out. The organism or species most likely to survive some set of circumstances is the one best equipped to endure those circumstances. What constitutes best equipment depends on the circumstances.
But phrases like "might makes right" and "live and let live" imply moralizations or moral obligations that simply don't have meaning when evaluating the laws of nature. "Might makes right" tries to say that because I'm bigger and stronger than you, whatever I might choose to do to you must be morally just. In fact my ability to enforce my will upon you has nothing to do with whether that will is just. The moral justification for keeping animals for food doesn't derive exclusively from our mere ability to do it.
Conversely "live and let live" suggests a moral framework where each species can and ought to live completely independent of one another. We agree it's morally desirable to invoke this policy where possible. But that doesn't imply it's always possible or always a moral absolute. If my living requires the use of other organisms -- which it does -- then I cannot simply let live. My living and its living are now practical opposites and therefore the maxim can't possibly be a moral absolute.